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A272574 a(n) = f(9, f(8, n)), where f(k,m) = floor(m*k/(k-1)).

%I A272574 #36 Sep 08 2022 08:46:16
%S A272574 0,1,2,3,4,5,6,9,10,11,12,13,14,15,18,19,20,21,22,23,24,27,28,29,30,
%T A272574 31,32,33,36,37,38,39,40,41,42,45,46,47,48,49,50,51,54,55,56,57,58,59,
%U A272574 60,63,64,65,66,67,68,69,72,73,74,75,76,77,78,81,82,83,84,85,86,87,90
%N A272574 a(n) = f(9, f(8, n)), where f(k,m) = floor(m*k/(k-1)).
%C A272574 Also, numbers that are congruent to {0..6} mod 9.
%C A272574 The initial terms coincide with those of A037475 and A039111. First disagreement is after 60 (index 48): a(49) = 63, A037475(49) = 81 and A039111(50) = 71.
%H A272574 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F A272574 G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + 3*x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
%F A272574 a(n) = a(n-1) + a(n-7) - a(n-8).
%F A272574 a(n) = (63*n - 12 - 12*(n mod 7) + 2*((-n-1) mod 7))/49. - _Wesley Ivan Hurt_, Dec 25 2016
%p A272574 f := (k, m) -> floor(m*k/(k-1)):
%p A272574 a := n -> f(9, f(8, n)):
%p A272574 seq(a(n), n = 0..70); # _Peter Luschny_, May 03 2016
%t A272574 f[k_, m_] := Floor[m*k/(k-1)];
%t A272574 a[n_] := f[9, f[8, n]];
%t A272574 Table[a[n], {n, 0, 70}] (* _Jean-François Alcover_, May 09 2016 *)
%t A272574 CoefficientList[Series[x (1 + x + x^2 + x^3 + x^4 + x^5 + 3 x^6)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)), {x, 0, 70}], x] (* or *)
%t A272574 Table[(63 n - 12 - 12 Mod[n, 7] + 2 Mod[-n - 1, 7])/49, {n, 0, 70}] (* _Michael De Vlieger_, Dec 25 2016 *)
%t A272574 LinearRecurrence[{1,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,9},90] (* _Harvey P. Dale_, May 08 2018 *)
%o A272574 (Magma) k:=9; f:=func<k,m | Floor(m*k/(k-1))>; [f(k,f(k-1,n)): n in [0..70]];
%o A272574 (Sage)
%o A272574 f = lambda k, m: floor(m*k/(k-1))
%o A272574 a = lambda n: f(9, f(8, n))
%o A272574 [a(n) for n in range(71)] # _Peter Luschny_, May 03 2016
%Y A272574 Cf. A248375: f(9,n).
%Y A272574 Cf. similar sequences with the formula f(k, f(k-1, n)): A008585 (k=3), A042948 (k=4), A047217 (k=5), A047246 (k=6), A047337 (k=7), A047602 (k=8), this sequence (k=9), A272576 (k=10).
%K A272574 nonn,easy
%O A272574 0,3
%A A272574 _Bruno Berselli_, May 03 2016